Evolution of long-lived globular cluster stars III. Effect of the initial helium spread on the position of stars in a synthetic Hertzsprung-Russell diagram

Context. Globular clusters host multiple populations of long-lived low-mass stars whose origin remains an open question. Several scenarios have been proposed to explain the associated photometric and spectroscopic peculiarities. They differ, for instance, in the maximum helium enrichment they predict for stars of the second population, which these stars can inherit at birth as the result of the internal pollution of the cluster by different types of stars of the first population. Aims. We present the distribution of helium-rich stars in present-day globular clusters as it is expected in the original framework of the fast-rotating massive stars scenario (FRMS) as first-population polluters. We focus on NGC 6752. (to be continued)